If the top ten nations were randomly selected to march, one after another, into the stadium at the closing ceremonies, in how many ways could the nations have marched in?

Answer:

90 degrees

Step-by-step explanation:

Same side interior angles, or consecutive angles, are supplementary (angle measures add up to 180 degrees). Since both angles have measures 3x degrees, the angles are congruent (same angle measure). In Geometry, when two angles are congruent and supplementary, the two angles are right angles (angles measuring 90 degrees). Therefore the angle measures of the two angles are 90 degrees and 90 degrees.

Or, to solve this algebraically, add 3x and 3x, let it equal to 180 degrees, solve for x, and find the angle measures by substituting x into the expression.

3x + 3x = 180

6x = 180

x = 30

3x = 3*30 = 90

Answer: C. - √2

Step-by-step explanation:

Given requirements from the question

Find the exact value of sec 135°

Convert into common trigonometric expression

sec = secant

secx = 1 / cosx

Therefore, sec 135° = 1 / (cos 135°)

Find the reference angle

135° is quite a complicated angle, but it is possible to simplify it by finding its reference angle.

Since 135° is in the second quadrant, its reference angle will be

                                         180° - 135° = 45°

However, we need to consider the positive and negative.

In a coordinate plane, the clue is (A S T C), which corresponds to the positive values in each quadrant. In the QI, "All" are positive. In the QII, sine is positive. In the QIII, the tangent is positive. In QIV, cosine is positive.

Therefore, when the value of cosine is in QII, it is negative.

The reference angle = - (1 / cos 45°)

Determine the final value

Given that the reference angle = - (1 / cos 45°)

cos 45° = 1 / √2

Therefore:

sec 135° = - (1 / cos 45°) = - (1 / (1 / √2)) = [tex]\boxed{-\sqrt{2} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The system of linear equations has at least one solution is consistent , whereas a system of linear equations that has no solution is inconsistent

What is a system of linear equations?

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

The subject of linear algebra, which is employed in most areas of contemporary mathematics, is based on the theory of linear systems. Numerical linear algebra includes computational strategies for obtaining the solutions, which are crucial to the fields of engineering, physics, chemistry, computer science, and economics. A helpful strategy when creating a mathematical model or computer simulation of a relatively complex system is to approximate a system of non-linear equations by a linear system (see linearization).

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Answer:

2^n

Step-by-step explanation:

So whenever you flip a coin, you can see it as 2 nodes branching off of each existing node. so for example when you flip a coin once you're going to have 2 sequences initially H and T, now when you flip a coin again for each of those 2 sequences 2 are going to branch off of that, making the total sequences 4, and the next flip 2 sequences are going to branch off each of the 4 sequences and so on. this can generally be described as: 2^n

I attached an image describing this a bit better but the bottom line is that for each 'end node'/sequence you're going to have 2 branch off of it, thus for each coin flip the number of sequences multiplies by 2

Answer:

2^n

Step-by-step explanation:

dont worry bout it ur welcome

Answer:

1/2

Step-by-step explanation:

50% = 50/100 = 1/2

1/2 of the students rode the first bus.

1 - 1/2 = 1/2

1/2 of the students rode the second bus.

The angle that vector makes with the x-axis is closest to [tex]340^\circ[/tex].

What is a vector?

An item with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.

If the magnitude and direction of two vectors match, they are the same vector. This indicates that if we take a vector and move it to a different point (without rotating it), the vector we finish up with is the same vector we started with.

Given,

[tex]x[/tex]-component of vector = 5.3

[tex]y[/tex]-component of vector = -2.3

angle = [tex]tan^{-1}(\frac{y}{x})[/tex]

angle = [tex]tan^{-1}(\frac{-2.3}{5.3} )[/tex]

angle = [tex]340^\circ[/tex]

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Answer:

x > -4

Step-by-step explanation:

[tex]2x+3 \geq 7 \\ \\

2x \geq 4 \\ \\

x \geq 2[/tex]

[tex]2x+9>1 \\ \\ 2x>-8 \\ \\ x>-4[/tex]

So, the union of these solutions is x > -4.

Answer:

8%

Step-by-step explanation:

The approximate difference between the theoretical and experimental probabilities for rolling an even number is 8%

Theoretical probability is what we expect to happen, whereas experimental probability is what actually happens when we try it out. The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes. As more trials are conducted, the experimental probability generally gets closer to the theoretical probability.

Theoretical probability of rolling a cube and getting a even number is 1/2 or 50% as number of odd numbers and number of even numbers are equal.

Experimental probability = Favorable outcomes/Total outcomes

Experimental probability = 10/24 = 5/12 ≅ 42%

Thus approximate difference between these two equals 50% - 42% = 8%

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From my analysis, the answer is likely to be D. I don't have a formula to prove it though.

Answer: 78 degrees.

Step-by-step explanation:

The other guy is wrong don't listen to him.

Here is the five-number summary:

Minimum: 9

Lower quartile:   11

Median: 24

Upper quartile:  34

Maximum: 45

Interquartile range: 23

The minimum number is the smallest number in the dataset. The  minimum number is 9. The maximum number is the largest number in the dataset. The maximum number is 45.

The first quartile, third quartile and the interquartile range are used to measure dispersion.

The first quartile : 1/4(n + 1)

1/4 x (12) = 3rd term = 11

The third quartile : 3/4 x (n + 1)

3/4 x (12) = 9th term = 34

Interquartile range = third quartile - first quartile

34 - 11 = 23

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

Median = 25

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Answer: [tex]\Large\boxed{15~dimes~;~9~nickels}[/tex]

Step-by-step explanation:

Given information

Number of coins = 24 coins

Total amount = $1.95

Dime = 10 cents = $0.1

Nickel = 5 cents = $0.05

Set variables

Let d be the number of dimes

Let n be the number of nickels

Set a system of equation

1) d + n = 24

2) 0.1d + 0.05n = 1.95

Multiply 10 on both sides of 2) equation

0.1d · 10 + 0.05n · 10 = 1.95 · 10

d + 0.5n = 19.5

Current system

1) d + n = 24

2) d + 0.5n = 19.5

Subtract 2) equation from the 1) equation

(d + n) - (d + 0.5n) = (24) - (19.5)

Expand the parenthesis

d + n - d - 0.5n = 24 - 19.5

Combine like terms

d - d + n - 0.5n = 4.5

0.5n = 4.5

Divide 0.5 on both sides

0.5n / 0.5 = 4.5 / 0.5

[tex]\Large\boxed{n=9}[/tex]

Substitute the n value into one of the equations to find the d value

d + n = 24

d + (9) = 24

d = 24 - 9

[tex]\Large\boxed{d=15}[/tex]

Hope this helps!! :)

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Answer: 21[tex]x^{2}[/tex] - 52x - 48

Step-by-step explanation:

Using the expanding rule we get

5x * 3x - 5x * 10 + (6[tex]x^{2}[/tex] - 18x + 16x -48)

15[tex]x^{2}[/tex] - 50x + 6[tex]x^{2}[/tex] - 2x - 48

21[tex]x^{2}[/tex] - 52x - 48

Answer:

21x^2-52x-48

Step-by-step explanation:

5x(3x-10) + (2x-6)(3x+8)

Distribute

5x^2 -50x+6x^2-2x-48

Combine like terms

21x^2-50x-2x-48

21x^2-52x-48

The given height of this trapezoid is given to be 4.5m

We have to solve for this by making use of the height of a trapezoid. The height is given as

A = (1/2) h (b1 + b2)

The variables here are

h = height

b1 = lenght at base 1

b2 = length at base 2

If the trapezoid that we have is a isosceles triangle, then base 1 is going to be the same length as that of the first base

b1 = 4 ft is the area. Given that the height has to be at least 4.5feet, then this would ensure that the trapezoid would be able to hold the shed.

Hence the height would begiven as 4.5 ft

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Answer: 4.5

Step-by-step explanation:

Answer:

a = 3

Step-by-step explanation:

4(2a - 3) = -2(a - 9)

8a - 12 = -2a + 18

10a = 30

a = 3

Let's check if we got it correct by substituting 3 for a in the original equation.

4(2*3 - 3) = -2(3 - 9)

4(6 - 3) = -2(-6)

4(3) = 12

12 = 12

Answer:

Step-by-step explanation:

Midpoint a point equidistant from the ends of a line or the extremities of a figure.

To find the midpoint of the line segment with endpoint, use the midpoint formula.

Midpoint formula:

[tex]\Rightarrow: \sf{\dfrac{x_2+x_1}{2}, \dfrac{y_2+y_1}{2} }}}[/tex]

y2=(-10)

y1=16

x2=6

x1=(-4)

Rewrite the problem down.

[tex]\sf{\left(\dfrac{6-4}{2},\:\dfrac{-10+16}{2}\right)}[/tex]

Solve.

6-4=2

2/2=1

-10+16=6

6/2=3

= (1,3)

Therefore, the correct answer is B (1,3).

I hope this helps, let me know if you have any questions.

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Answer:

When dividing both sides by a negative.

Step-by-step explanation:

When dividing OR multiplying both sides by a negative, we need to flip the inequality signs.

Answer:

(A∩B)' = A'∪B'

Step-by-step explanation:

U is the universal set

A and B are two subsets of U

let A' be the complement subset of A

and  B' be the complement subset of B

U = {-10,-9,…,-1,0,1,…,9,10}

A = {-1,0,1}

B = {1,2,…,9,10}

Then

A∩B = {1}

Then

the complement of A∩B :

(A∩B)' = {-10,-9,…,-1,0,2,…,9,10}

(notice the absence of 1)

On the other hand,

A' = {-10,…,-2}∪{2,…,10}

B' = {-10,…,0}

Then

A'∪B' = {-10,-9,…,-1,0}∪{2,…,10}

         =  {-10,-9,…,-1,0,2,…,9,10}

Conclusion:

(A∩B)' = A'∪B'

The solution to the system of equations that includes functions f(x) and g(x) is given by: (1,7).

A linear function is modeled by:

y = mx + b

In which:

The linear function g(x) goes through point (0,5), hence the y-intercept is of 5. The function also goes through point (1,7), hence the slope is of 2 and the function is:

g(x) = 5 + 2x.

The solution to the system of equations is found as follows:

f(x) = g(x)

2x² + x + 4 = 5 + 2x

2x² - x - 1 = 0

Which is a quadratic equation with coefficient a = 2, b = -1, c = -1, hence:

When x = 1, f(x) = g(x) = 7, hence the solution of the system is of (1,7).

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Answer:

D. (1,7)

Step-by-step explanation:

I took the exam

Answer:

8 pi yd.

Step-by-step explanation:

The circumference of a circle can be calculated as follows:

c = [tex]2 \cdot \pi \cdot r[/tex]

Where r is the radius of the circumference.

So in our case:

c = [tex]2 \cdot \pi \cdot 4yd = 8\cdot \pi[/tex] yd.

The circumference of the circle, in the attached image is approximately 25.1 yards.

To find the circumference of a circle, you can use the formula:

Circumference = 2 * π * radius

where π = 3.14159.

Given the radius of the circle is 4 yards, the circumference can be calculated as follows:

Circumference = 2 * 3.14159 * 4 yards ≈ 25.13272 yards

Now, rounding to the nearest tenth, the circumference of the circle is approximately 25.1 yards.

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Using it's concept, the experimental probability of getting an odd number and a number greater than 6 is given by:

1/5.

A probability is given by the number of desired outcomes divided by the number of total outcomes. An experimental probability is calculated considering the results of previous trials.

In this problem, there are 10 trials, and of those, 2 of them, trial 8 and trial 10, resulted in an odd number and a number greater than 6, hence the probability is:

p = 2/10 = 1/5.

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The statement that <A > <C and <B > <D has been proved

In geometry, the side length opposite the largest angle is the longest side.

Similarly, the side length opposite the smallest angle is the shortest side.

From the given figure of quadrilateral, we have the following sides in increasing order:

The angles opposite the side lengths are:

This means that:

<A > <C and <B > <D

Hence, the statement that <A > <C and <B > <D has been proved

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Answer:

3

Step-by-step explanation:

f(x)-g(x)=3-cos(x)

when u limit it

u have

3-cos180

which is 3-0

3

The order that will result in a final output of -31 when the first input is 0 is as follows; Third → Second → Fourth → First

First gives;

y = -2·x + 34 = 18

Second gives;

y = -x/3 - 10 = -38/3

Third gives;

= -24

Fourth gives;

y = (x - 2)² = 36

We have after several iterations;

Third gives,

= -24

Next we input into the second to get,

y = -(-24)/3 - 10 = 24/3 - 10 = 8 - 10 = -2

Next we input into the fourth to get,

y = ((-2) - 2)² =  (-4)² = 16

Next we input into the first to get,

y = -2×16 + 34 = -32 + 34 = 2

Which gives the order as follows;

Third → Second → Fourth → First

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The simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)

The expression is given as:

(2x+1)/(x²-3)

The above expression is a fraction and the numerator has 2 terms

For a fraction

A + B)/x

The fraction can be split as

A/x + B/x

Using the above as a guide, we have:

(2x+1)/(x²-3) = 2x/(x²-3) + 1/(x²-3)

Hence, the simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)

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I'll go for 40.

To find the value of y,

draw a line up from the x - axis at 1910,

all the way up to cross the blue line;

then, draw a horizontal line from the point where the recent line meets the blue one.

Now read of the value you get for y.

Hope this helps!

Answer:

x = 1; y = a

Step-by-step explanation:

ax+y=2a

x+ay=1+a^2

-a²x-ay=-2a²

x+ay=1+a^2

(1 - a²)x = 1 - a²

x = (1 - a²)/(1 - a²)

x = 1

a + y = 2a

1 + ay = 1 + a²

a = y

x = 1; y = a

The expressions 14, 6 + 8, and (6 + 8) are equivalent because they are all equal to 1

14

6 + 8

= 14

(6 + 8)

= 14

The coefficient of (6 + 8) is 1, so, the expression remains the same.

Equivalent expressions refers to those expressions that work the same even though they look different.

The importance or significance of equivalent expression is that its makes expressions easier to work with and solve.

Therefore, the expressions 14, 6 + 8, and (6 + 8) are all equivalent to 14.

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